A first order linear differential equation has the following form:

The general solution is given by

where

called the integrating factor. If an initial condition is given, use it to find the constant C.

Here are some practical steps to follow:

1. If the differential equation is given as

rewrite it in the form

where

2. Find the integrating factor

3. Evaluate the integral

4. Write down the general solution

5. If you are given an IVP, use the initial condition to find the constant C.




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